Abstract
The worldline formalism is a useful scheme in Quantum Field Theory which has also become a powerful tool for numerical computations. It is based on the first quantisation of a point-particle whose transition amplitudes correspond to the heat-kernel of the operator of quantum fluctuations of the field theory. However, to study a quantum field theory in a bounded manifold one needs to restrict the path integration domain of the point-particle to a specific subset of worldlines enclosed by those boundaries. In the present article it is shown how to implement this restriction for the case of a spinor field in a two-dimensional curved half-plane under MIT bag boundary conditions, and compute the first few heat-kernel coefficients as a verification of the proposed construction. This construction admits several generalisations.
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Acknowledgments
The author thanks Santiago Christiansen Murguizur, Horacio Falomir, Joaquín Liniado and Pablo Pisani for valuable discussions during the research. This work was supported by CONICET (under the program “Becas Internas Doctorales”, RESOL-2020-129-APN-DIR#CONICET) and UNLP (under project 11/X909).
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Manzo, L. Worldline approach for spinor fields in manifolds with boundaries. J. High Energ. Phys. 2024, 144 (2024). https://doi.org/10.1007/JHEP06(2024)144
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DOI: https://doi.org/10.1007/JHEP06(2024)144